I want to create tabbed ActionBar (NAVIGATION_MODE_TABS) with custom view (DISPLAY_SHOW_CUSTOM). It should looks like this:

I just need to be able to navigate through the activities via buttons in the top row – as I would do with ActionBar in normal – non tabbed mode, and also be able to switch tabs in second row. If I set ActionBar to be in a tabbed mode, the custom view disappears, it seems that tabbed mode and custom view are mutually exclusive… Is it even possible?
There are more possible ways how to do that without ActionBar. Normally I would create a layout with buttons, include it in the TabActivity (which is now deprecated) and that’s all. But I do not feel it would be the best solution, so any help or advice is appreciated.
Thanks in advance.
EDIT: After a little research I found that it works, it is just not gets displayed on my 4 inch screen. However it still does not work as I expected. On wider screens a custom view shows on the right side of the tabs – it is ok, but on the 4 inch phone screens it is not displayed at all.
I think the best solution is to use ActionBarSherlock library (I do not like using deprecated features and my app must work also on pre – sdk11 version devices) and fragments – one for top ActionBar and the second for tabbed view.
The buttons in the top row have to be added as optionMenu items:
The philosophy of the ActionBar is slightly different then I supposed to be when asking. From the Android developer guide:
When you want to provide navigation tabs in an activity, using the action bar’s tabs is a great option (instead of using TabWidget), because the system adapts the action bar tabs for different screen sizes—placing them in the main action bar when the screen is sufficiently wide, or in a separate bar (known as the “stacked action bar”) when the screen is too narrow.